# Stem and leaf diagrams Sometimes called ‘stem and leaves’ too.

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Stem and leaf diagrams Sometimes called ‘stem and leaves’ too

They really are as simple as they seem

Simply a way of showing the values of data

Example…….. Here are the weights of some aardvarks (kg): 12, 28, 17, 17, 19, 23, 9, 7, 25, 34, 21 Stem and leaf might look like this: Weight of aardvarks 0 9, 7 12, 7, 7, 9, 28, 3, 5, 1 KEY 34 1 2 is 12kg STEMLEAF OR LEAVES Don’t need to write this usually

Your ‘stem and leaf’ must have a… 1.Title 2.Key – so that other people can work out what your values are.

An ordered ‘stem and leaf’…. Has the values in size order.

So for our example before… Weight of aardvarks 0 9, 7 12, 7, 7, 9, 28, 3, 5, 1 KEY 34 1 2 is 12kg The ordered ‘stem and leaf’ would be: Weight of aardvarks 0 7, 9 12, 7, 7, 9, 21, 3, 5, 8 KEY 34 1 2 is 12kg What weight does the ‘5’ represent?

Show the following data as a stem and leaf diagram I.Q. scores of Year 10 girls: 105, 98, 112, 94, 130, 121, 98, 104, 100, 108, 112, 104, 101, 97, 104 I.Q. scores of Year 10 girls 9 8, 4, 8, 7 10 5, 4, 0, 8, 4, 1, 4 11 2, 2 12 1 13 0 KEY 11 2 means 112

Now ‘order it’ I.Q. scores of Year 10 girls (unordered) 9 8, 4, 8, 7 10 5, 4, 0, 8, 4, 1, 4 11 2, 2 12 1 13 0 KEY 11 2 means 112 I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

The ordered one can be used to find lots of information

Mode…. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 Mode – most common In this case 104

Range …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 Highest value – lowest value In this case: Range = 130 – 94 = 36

Median …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the middle value In this case we have 15 values so we want the median = 104 8 th value along

Lower Quartile …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value a quarter of the way up In this case we have 15 values so we want the Lower quartile = 98 4 th value along

Upper Quartile …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value three- quarters of the way up In this case we have 15 values so we want the Upper quartile = 112 12 th value along

You now know enough to be able to draw a ‘box and whisker diagram’ Smallest value Largest value median Lower quartile upper quartile 90 100 110 120 130 I.Q. Score

Now for the boys……..

Show the following data as a stem and leaf diagram I.Q. scores of Year 10 boys: 103, 98, 112, 99, 108, 122, 98, 104, 100, 108, 112, 104, 101, 97, 104, 108, 99, 108, 102 I.Q. scores of Year 10 boys 9 8, 9, 8, 7, 9 10 3,8,4,0,8,4,1,4,8,8,2 11 2, 2 12 2 KEY 11 2 means 112

Now ‘order it’ I.Q. scores of Year 10 boys (unordered) 9 8, 9, 8, 7, 9 10 3,8,4,0,8,4,1,4,8,8,2 11 2, 2 12 2 KEY 11 2 means 112 I.Q. scores of Year 10 boys (ordered) 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112

Mode …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 Mode – most common In this case 108

Range …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 Highest value – lowest value In this case: Range = 122 – 97 = 25

Median …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the middle value In this case we have 19 values so we want the median = 104 10 th value

Lower Quartile …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value a quarter of the way up In this case we have 19 values so we want the Lower quartile = 99 5 th value

Upper Quartile …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value three- quarters of the way up In this case we have 19 values so we want the Upper quartile = 108 15 th value

Now draw a box and whisker diagram to compare the I.Q. of boys and girls you can draw this one on the same diagram as before.

Here we go ….. 90 100 110 120 130 I.Q. Score GIRLS BOYS What can you say about boys and girls I.Q.s ?

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